How an entropic uncertainty relation breaks down?

This work is devoted to the question of whether information-based uncertainty relations, especially Deutsch's inequality, could be a better alternative than standard deviation-based uncertainty relations. We use two filter-type experiments in which a single half-spin particle passes through two Stern-Gerlach apparatuses in two successive times. In the first experiment the apparatuses are orthogonal, while in the second experiment as a general case, the apparatuses are arbitrarily arranged. We show that for the second experiment Deutsch's inequality doesn't satisfy the quantum uncertainty and is violated.